Question

The equation of the straight line passing through the point $(3,2)$ and perpendicular to the line $y=x$ is

• A. $x-y=5$
• B. $x+y=5$
• C. $x+y=1$
• D. $x-y=1$

Answer 1

The correct option is B

$x+y=5$

Form the equation of the straight line based on given information

Given, the line is passing through the point $(3,2)$) and It is perpendicular to line $y=x$.

By comparing the given equation of line with the equation of line in slope-intercept form $y=mx+c$ we get,

The slope of the given line $m_1=1$.

We know that if the lines are perpendicular to each other then the product of their slopes is $-1$

So the slope of the required line is $m=-1$.

We also know that the equation of line in point slope form is given by: $y-y_1=m\left(x-x_1\right)$

So we have $(x_1,y_1)=(3,2)$ and $m=-1$

By substituting the values we get,

$$\begin{gathered} y-2=-1\left(x-3\right) \\ \Rightarrow y-2=-x+3 \\ \Rightarrow x+y=5 \end{gathered}$$

So, the equation of the straight line passing through the point $(3,2)$ and perpendicular to the line $y=x$ is $x+y=5$ .

Hence, the correct answer is option (B).